Vector Calculus and Exercises | LA | Course

Brief Information
  • Name : Vector Calculus and Exercises
  • Lecturer : 강영옥
  • Semester : 2014 Winter
  • Course : Liberal arts
  • Textbook
    1. 송영권, 송형수, 이종우, 이흥수, 지은숙, 허민 (2009) 벡터해석. 교우사
    2. Thomas, G., B. (2006) 미분적분학. 11 Ed. 자유아카데미
  • Syllabus : Syllabus__Vector Calculus and Exercises
  • In short
Supplements for self-study
  • Murray R. Spiegel, Seymour Lipschutz, and Denis Spellman. (2009) Vector Analysis. McGraw-Hill
Trace lectures
  • 3 coordinate systems: rectangular/cylindrical/spherical coordinate system
  • scalar and vector
  • vector space
  • projection
  • dot product, cross product
  • triple product
  • equation of lines
  • equation of planes
  • vector function
  • limit of vector functions
  • continuity of vector functions
  • curve
  • position vector X
  • parametric curve
  • tangent vectors of a curve, an unit tangent vectors T
  • length of a curve
  • parametric equation by length parameter
  • curvature kappa
  • radius of curvature, circle of curvature
  • principal unit normal vector N
  • unit binormal vector B
  • function of several variables, multivariate function
  • level curve, level surface
  • limit of multivariate functions
  • continuity of multivariate functions
  • partial differentiation of multivariate functions, partial derivative, second order partial derivative
  • ordinary differentiation of multivariate functions
  • tangent plane
  • linear approximation, true value, approximate value, error, absolute error, relative error, percentage error
  • chain rule when differentiation of multivariate functions
  • differentiation of implicit functions
  • gradient of multivariate functions
  • directional derivative of multivariate functions on a directional vector
  • tangent plane described by gradient, normal line described by gradient
  • extremums of multivariate functions, extreme point
  • maximum, maximal point, minimum, minimal point
  • critical point
  • saddle point
  • determinant of a critical point if an extremum (?)
  • double integral, iterated integral
  • Fubini’s Theorem
  • double integral on polar coordinate
  • midterm exam
  • final exam
Assignments
  1. Solve Exercises 1.1 ~ 3.3 (2014-12-26~27)
    [1.1] 2-3, 3-5, 6-2, 6-5, 7-2, 8-2
    [1.2] 4, 5, 6
    [1.3] 3, 5, 8, 9
    [2.1] 1-1, 1-3, 5-2, 7
    [2.2] 2, 3, 6, 13-3, 13-6
    [3.2] 2, 3-4, 5
    [3.3] 2, 6, 10
  2. Solve Exercises 3.4 ~ 4.1 (2014-12-28~2015-01-02)
    [3.4] 2, 3-2, 5, 8
    [3.5] 1-2, 1-3, 3-2, 5
    [3.6] 2-4, 8, 10
    [3.7] 1-3, 1-5
    [4.1] 2-5, 2-6, 2-7, 3-2, 3-3, 3-4, 4-2, 6, 8, 10-2, 10-3
Summarize themes
  • position vector, velocity, acceleration

 

Leave a Reply

Your email address will not be published. Required fields are marked *